Two interacting Hofstadter butterflies

The problem of two interacting particles in a quasiperiodic potential is addressed. Using analytical and numerical methods, we explore the spectral properties and eigenstates structure from the weak to the strong interaction case. More precisely, a semiclassical approach based on non commutative geometry techniques permits to understand the intricate structure of such a spectrum. An interaction induced localization effect is furthermore emphasized. We discuss the application of our results on a two-dimensional model of two particles in a uniform magnetic field with on-site interaction.Comment: revtex, 12 pages, 11 figure

Role of chaos for the validity of statistical mechanics laws: diffusion and conduction

Several years after the pioneering work by Fermi Pasta and Ulam, fundamental questions about the link between dynamical and statistical properties remain still open in modern statistical mechanics. Particularly controversial is the role of deterministic chaos for the validity and consistency of statistical approaches. This contribution reexamines such a debated issue taking inspiration from the problem of diffusion and heat conduction in deterministic systems. Is microscopic chaos a necessary ingredient to observe such macroscopic phenomena?Comment: Latex, 27 pages, 10 eps-figures. Proceedings of the Conference "FPU 50 years since" Rome 7-8 May 200

Kinase Targets for Mycolic Acid Biosynthesis in Mycobacterium tuberculosis.

Mycolic acids (MAs) are the characteristic, integral building blocks for the mycomembrane belonging to the insidious bacterial pathogen Mycobacterium tuberculosis (M.tb). These C60-C90 long a-alkyl-ß-hydroxylated fatty acids provide protection to the tubercule bacilli against the outside threats, thus allowing its survival, virulence and resistance to the current antibacterial agents. In the post-genomic era, progress has been made towards understanding the crucial enzymatic machineries involved in the biosynthesis of MAs in M.tb in which two discrete fatty acid synthases systems (FAS-I and FAS-II) were discovered. However, gaps still remain in the exact role of the phosphorylation and dephosphorylation regulatory mechanisms within these systems. To date, a total of 11 serine-threonine protein kinases (STPKs) are found in M.tb. Most enzymes implicated in the MAs synthesis were found to be phosphorylated in vitro and/or in vivo. For instance, phosphorylation of KasA, KasB, mtFabH, HadAB/BC, InhA, MabA, FadD32 and PcA downregulated their enzymatic activity, while phosphorylation of VirS increased its enzymatic activity. These observations suggest that the kinases and phosphatases system could play a role in M.tb adaptive responses and survival mechanisms in the human host. As the mycobacterial STPKs do not share a high sequence homology to the human's, there has been some early drug discovery efforts towards developing potent and selective inhibitors as novel antitubercular agents. Recent updates to the kinases and phosphatases involved in the regulation of MAs biosynthesis will be presented in this minireview, including their known small molecule inhibitors